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1.
The angular velocity of the earth with which it has to rotate so that acceleration due to gravity on 
latitude becomes zero is (Radius of earth 
At the poles 
)
latitude becomes zero is (Radius of earth At the poles )
2.
In a satellite, if the time of revolution is 
then KE is proportional to
then KE is proportional to
3.
Three identical bodies of mass 
are located at the vertices of an equilateral triangle of side 
. They revolve under the effect of mutual gravitational force in a circular orbit, circumscribing the triangle while preserving the equilateral triangle. Their orbital velocity is
are located at the vertices of an equilateral triangle of side . They revolve under the effect of mutual gravitational force in a circular orbit, circumscribing the triangle while preserving the equilateral triangle. Their orbital velocity is
4.
Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is 
and that on the surface of the new planet is 
, then
and that on the surface of the new planet is , then
5.
An artificial satellite of the earth moves at an altitude to 
km along a circular orbit. The velocity of the satellite is
km along a circular orbit. The velocity of the satellite is
6.
Escape velocity of a body of 
mass on a planet is 
. Gravitational Potential energy of the body at the Planet is
mass on a planet is . Gravitational Potential energy of the body at the Planet is
7.
A particle of mass 
is placed at the centre of a uniform spherical shell of mass 3 and radius 
. The gravitational potential on the surface of the shell is
is placed at the centre of a uniform spherical shell of mass 3 and radius . The gravitational potential on the surface of the shell is
8.
The work that must be done in lifting a body of weight 
from the surface of the earth to a height 
is
from the surface of the earth to a height is
9.
Two spherical planets 
and 
have same mass but densities in the ratio 8:1. For these planets, the ratio of acceleration due to gravity at the surface of to its value at the surface of is
and have same mass but densities in the ratio 8:1. For these planets, the ratio of acceleration due to gravity at the surface of to its value at the surface of is
10.
A satellite which is geostationary in a particular orbit is taken to another orbit. Its distance from the centre of earth in new orbit is 2 times that of the earlier orbit. The time period in the second orbit is